We propose a new reduced model for gravity-driven free-surface flows of shallow viscoelastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for viscoelastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. Additionally to the classical layer depth and velocity i...

Atomic layer deposition sALDd has become an essential technique for fabricating nano-scale thin films in the microelectronics industry, and its applications have been extended to multicomponent thin films, as well as to single metal oxide and nitride films. A mathematical film growth model for ALD is proposed to predict the deposition characteristics of multicomponent thin films grown mainly in...

This paper is concerned with an investigation into the localized instability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and under different boundary conditions of clamped, hinged, sliding contact and free on the other edge, is studied. A mathematical model is used and a general solution is presented. The conditions unde...

We study a model electrochemical thin film at DC currents exceeding the classical diffusion-limited value. The mathematical problem involves the steady Poisson–Nernst–Planck equations for a binary electrolyte with nonlinear boundary conditions for reaction kinetics and Stern-layer capacitance, as well as an integral constraint on the number of anions. At the limiting current, we find a nested b...